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Neighbors (Posted on 2014-04-18) Difficulty: 2 of 5
Find the smallest integer n such that both n-1 and n+1 have the same number of divisors as n.
Bonus task: List few additional numbers with said feature.

See The Solution Submitted by Ady TZIDON    
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re: computer solution | Comment 6 of 8 |
(In reply to computer solution by Charlie)

Nice list.  A quick scan shows that there are not only triples with the same number of divisors but also quartets: 242, 243, 244, 245 and a few others.  (none of semi-primes, or course.)  An additional OEIS sequence would be appropriate.

I didn't notice any quintets.  Care to search further?

Looking at the number of factors column, there are of course no odds.  Also no 10 which isn't too surprising - you'd need 3 consecutive numbers with factors that are 4th powers.

  Posted by Jer on 2014-04-18 14:08:50

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